which was studied by Tao and Candès [1]}.
Problem (REF ) can be seen as an instance of REF  with \(f\equiv 0\) .
Since we need some second order information for our local Newton-type methods, instead of the noise-free problem (REF ) we are more interested in the problem
\( \min _x \ \left\Vert x\right\Vert _0 \quad \text{s.t.}\quad \left\Vert Ax - \overline{b}\right\Vert _2 \le \delta ,\) 
